That was actually the first thing I googled for. Apparently, though, "Prufer" is the more common Anglicism, and neither produced any useful introductory documents.

So what the hell, I'll give it a shot.

The idea is to generate a unique sequence for each labelled tree on N vertices. What you end up doing is removing vertices one at a time, starting with the highest label leaf vertex (you can start with the lowest, it doesn't matter, as long as you're consistent). When you remove a vertex, you add the label of the vertex it was adjacent to to the sequence. Keep going until you only have two vertices left. You've got a Prüfer sequence!